# Ballistic Missiles Trajectories Questions and Answers

This set of Spaceflight Mechanics Multiple Choice Questions & Answers (MCQs) focuses on “Ballistic Missiles Trajectories”.

1. Which of these trajectories is followed by the ballistic missile?
a) Orbital trajectory
b) Ballistic trajectory
c) Planetary trajectory
d) Aft-crossing trajectory

Explanation: A ballistic missile trajectory is used by missiles for warfare purposes. It is different from the orbit followed by the satellite as the ballistic missile trajectory intersects the Earth’s surface. The trajectory comprises of three portions-powered flight regime, free flight regime and the re-entry regime.

2. In which aspect does the trajectory of missile differ from the satellite’s orbit?
a) It intersects the earth’s surface
b) It follows a parabolic path
c) It stays within the earth’s atmosphere
d) It has a brief time of period

Explanation: The trajectory of a missile differs from a satellite orbit in only one respect-it intersects the surface of the Earth at two places. If we consider only the free-flight portion of the ballistic missile trajectory, then it follows the conic orbit just like a satellite.

3. Which of these portions is not a part of ballistic trajectory?
a) Powered flight portion
b) Free flight portion
c) Re-entry portion
d) Cruise portion

Explanation: The ballistic trajectory is composed of three components-powered flight portion which is comprises of path from launch to the burnout, free-flight portion which constituted most of the trajectory and the re-entry portion which lasts until the impact.

4. During the powered flight and re-entry, flight is analyzed using two-body mechanics.
a) True
b) False

Explanation: During powered flight and re-entry there are continuous external forces other than gravity on the missile, so these parts of the flight cannot be analyzed with two-body mechanics. Free-flight range equation, flight-path angle equation and maximum range trajectory are used respectively.

5. What is the value of the non-dimensional parameter (Q) for a circular orbit?
a) 1
b) 2
c) 3
d) 0

Explanation: Q is the non-dimensional parameter whose formula is given by: Q ≡ $$\Big(\frac{v}{v_{cs}}\Big)^2 = \frac{v^2 r}{\mu}$$
The energy equation is given by: ε = $$\frac{v^2}{2} – \frac{\mu}{r} = -\frac{\mu}{2a}$$
On substituting the value of $$\frac{\mu Q}{r}$$ for v2 we get Q = 2 – $$\frac{r}{a}$$
Q = 1 exists at every point in a circular orbit and at the end of the minor axis of every elliptical orbit.

6. What is the value of the non-dimensional parameter (Q) for a satellite that has escape speed and is on a parabolic orbit?
a) 0
b) 1
c) 2
d) 3

Explanation: The value of non-dimensional parameter varies from point to point in an orbit. The value of the parameter for a satellite that has an escape speed and is on the path of the parabolic path is 2. Q=1 is the condition for circular orbit.

7. If the satellite is in a hyperbolic orbit. What is the value of the non-dimensional parameter (Q)?
a) 0
b) 1
c) 2
d) > 2

Explanation: The non-dimensional parameter at a point in the orbit is given by the squared ratio of speed of satellite to satellite speed in the circular orbit at that point. When the value of Q is greater than 2, the satellite follows a hyperbolic path which is very rare.

8. What is the trajectory called which corresponds to the higher value of flight-path angle?
a) Low trajectory
b) High trajectory
c) Medium trajectory
d) Controlled trajectory

Explanation: The formula for the flight path angle is given by:
sin$$($$2ϕbo + $$\frac{\psi}{2}) = \frac{2 – Q_{bo}}{Q_{bo}}$$ sin $$\frac{\psi}{2}$$
Using the formula, there are two angles with the calculated sine since the equation has two solutions. The trajectory corresponding to the larger value of flight-path angle is called the high trajectory.

9. What is the trajectory called which corresponds to the lower value of flight-path angle?
a) Low trajectory
b) High trajectory
c) Medium trajectory
d) Controlled trajectory

Explanation: Flight path for a trajectory yields two solutions. The solution having the smaller value is known as the low trajectory and the solution with higher value is known as the high trajectory. The nature of high or low trajectory is dependent on the value of Qbo.

10. Which of these assumptions is used to find the ballistic missile trajectory equations?
a) Free flight trajectory is asymmetrical
b) Rotation of the earth is ignored
c) Oblations of the earth is ignored
d) The speed of missile stays constant

Explanation: In order to derive the ballistic missile trajectory equations, there are two assumptions made. First is that the rotation of the earth is ignored and second is that the free-flight trajectory is assumed to be symmetrical.

More MCQs on Ballistic Missiles Trajectories:

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